Related papers: Simplifying Algebra in Feynman Graphs, Part III: M…
We prove a neat factorization property of Feynman graphs in covariant perturbation theory. The contribution of the graph to the effective action is written as a product of a massless scalar momentum integral that only depends on the basic…
We propose a symmetry law for a doublet of different form fields, which resembles gauge transformations for matter fields. This may be done for general Lie groups, resulting in an extension of Lie algebras and group manifolds. It is also…
Based on our recent findings regarding (non-)renormalizability of non-commutative U*(1) gauge theories [arxiv:0908.0467, arxiv:0908.1743] we present the construction of a new type of model. By introducing a soft breaking term in such a way…
The relation for the gravity polarisation tensor as the tensor product of two gluon polarisation vectors has been well-known for a long time, but a version of this relation for multi-particle fields is presently still not known. Here we…
This work deals with the theory of a quantized spin-2 field in the framework of causal perturbation theory. It is divided into two parts. In the first part we analyze the gauge structure of a massless self-interacting quantum tensor field.…
We continue the study of symmetries in the Lagrangian formalism of arbitrary order with the help of the so-called Anderson-Duchamp-Krupka equations. For the case of second-order equations and arbitrary vector fields we are able to establish…
The concept of electric-magnetic duality can be extended to linearized gravity. It has indeed been established that in four dimensions, the Pauli-Fierz action (quadratic part of the Einstein-Hilbert action) can be cast in a form that is…
Recently a reformulation of the MHV diagram method in N=4 supersymmetric Yang-Mills theory in momentum twistor space was presented and was shown to be equivalent to the perturbative expansion of the expectation value of a supersymmetric…
For any given sequence of integers there exists a quantum field theory whose Feynman rules produce that sequence. An example is illustrated for the Stirling numbers. The method employed here offers a new direction in combinatorics and graph…
This paper will describe how combinatorial interpretations can help us understand the algebraic structure of two aspects of perturbative quantum field theory, namely analytic Dyson-Schwinger equations and periods of scalar Feynman graphs.…
An iterative Noether scheme, advocated by Deser, is used to introduce gauge invariant couplings to nonrelativistic matter with global symmetries related to usual charge conservation and dipole conservation recently discussed in fractonic…
The idea of gauging (i.e. making local) symmetries of a physical system is a central feature of many modern field theories. Usually, one starts with a Lagrangian for some scalar or spinor matter fields, with the Lagrangian being invariant…
Bosonization of the gauged, massive Thirring model in 2+1-dimensions produces a Maxwell-Chern-Simons gauge theory, coupled to a dynamical, massive vector field. Exploiting the Master Lagrangian formalism, two dual theories are constructed,…
New algebraic approach to analytical calculations of D-dimensional integrals for multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of multi-loop Feynman integrals, such as integration by parts…
We present a method to automatically derive the Feynman rules for mesonic chiral perturbation theory with a lattice regulator. The Feynman rules can be output both in a human-readable format and in a form suitable for an automated numerical…
We consider, at the linearized level, the superspace formulation of lower-dimensional F-theory. In particular, we describe the embedding of 3D Type II supergravity of the superstring, or 4D, N=1 supergravity of M-theory, into the…
Based on the gauge invariant variables proposed in our previous paper [K. Nakamura, Prog. Theor. Phys. vol.110 (2003), 723.], some formulae of the perturbative curvatures of each order are derived. We follow the general framework of the…
We propose a graded classification of the entire field of multivector physics, including all alternative points of view. The (often tacit) postulates of different types of formulations are contrasted, summarizing their consequences.…
We discuss the Hamiltonian formulation of the Schwinger proper-time method of calculating Green functions in gauge theories. Instead of calculating Feynman diagrams, we solve the corresponding Dyson-Schwinger equations. We express the…
The Lie algebra of Feynman graphs gives rise to two natural representations, acting as derivations on the commutative Hopf algebra of Feynman graphs, by creating or eliminating subgraphs. Insertions and eliminations do not commute, but…